Counting conjugacy classes in Sylow p-subgroups of Chevalley groups

• Autores: Simon M. Goodwin
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 210, Nº 1, 2007, págs. 201-218
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2006.09.009
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• Resumen

  • Let p be a prime and let q be a power of p. Let U(q) be a Sylow p-subgroup of a finite Chevalley group G(q) and let B(q) be the normalizer of U(q) in G(q). In this paper we prove rationality of the zeta functions associated to: the number of conjugacy classes of U(q); the number of B(q)-conjugacy classes in U(q); and the number of conjugacy classes of B(q). Our proof is constructive and provides a parametrization of the conjugacy classes; it also leads to a method to calculate the zeta functions.